A robot arm is moving in a defined space. Using ultrasonic sensors calculate the
coordinate of the robot end effector position. A transmitter T1 is attached at the end
effector of the robot arm and two receivers R1 and R2 are placed 2m away from each
other as shown in Figure. The speed of sound is 340m/s in the air. R1 detects signal
from the transmitter T1 after 5ms and, R2 detects signal from the transmitter T1 after
3ms. Using a triangulation method calculate the end effector x and y coordinate of the
robot arm.

To save energy, the air supply to a 2000 ft office has been shut off overnight and the room temperature has dropped to 40°f. in the morning, the thermostat is reset to 70°f and warm air at 120 f begins to flov in at 200ft'/min. the air is well mixed within the room, and an equal mass flow of air at room temperature (changing with time) is withdrawn through a return duct. the air pressure is nearly 1 atm everywhere. ignoring heat transfer with the surroundings and kinetic and potential energy effects, estimate how long it takes for the room temperature to reach 70°f. plot the room temperature as a function of time.